Series: Understanding Complex Systems
2008, Approx. 250 p., Hardcover
ISBN: 978-3-540-75559-3
About this book
Effective evacuation of people from closed spaces is an extremely important topic, since it can save real lives in emergency situations that can be brought about by natural and human made disasters. Usually there are static maps posted at various places at buildings that illustrate routes that should be taken during emergencies. However, when disasters happen, some of these routes might not be valid because of structural problems due to the disaster itself and more importantly because of the distribution of congestion of people spread over the area. The average flow of traffic depends on the traffic density. Therefore, if all the people follow the same route, or follow a route without knowing the congestion situation, they can end up being part of the congestion which results in very low flow rate or worse a traffic jam. Hence it becomes extremely important to design evacuations that inform people how fast and in which direction to move based on real-time information obtained about the people distribution using various sensors. The sensors used can include cameras, infra red sensors etc., and the technology used to inform people about the desired movement can be communicated using light matrix, small speakers, and in the future using wireless PDAs. This book provides mathematical models of pedestrian movements that can be used specifically for designing feedback control laws for effective evacuation. The book also provides various feedback control laws to accomplish the effective evacuation. The book uses the hydrodynamic hyperbolic PDE macroscopic pedestrian models since they are amenable to feedback control design. The control designs are obtained through different nonlinear techniques including Lyapunov functional techniques, feedback linearization in the distributed model, and some discretized techniques.
Table of contents
Traffic Flow Theory For 1-D.- Crowd Models for 2-D.- Numerical Methods.- Feedback Linearization (1D Patches).- Intelligent Evacuation Systems.- Discretized Feedback Control.- Discretized Optimal Control.- Distributed Feedback Control 1D.- Distributed Feedback Control 2D.- Robust Feedback Control.
Series: Modern Birkhauser Classics
Softcover reprint of the 1995 2nd ed., 2008, XIV, 412 p. 7 illus., Softcover
ISBN: 978-0-8176-4756-8
About this book
An affordable new softcover edition of a bestselling text
Devoted to one of the fastest developing fields in modern control theory?H-infinity optimal control theory
Contains original results, based on the authors' research
For a broad audience of graduate students, researchers and practitioners in applied mathematics, control, and dynamic games
May be used as a textbook in a second-level graduate course in control curriculum
Table of contents
Preface.- A General Introduction to Minimax Designs.- Basic Elements of Static and Dynamic Games.- The Discrete-Time Minimax Design Problem With Perfect State Measurements.- Continuous-Time Systems With Perfect State Measurements.- The Continuous-Time Problem With Imperfect State Measurements.- The Discrete-Time Problem With Imperfect State Measurements.- Performance Levels for Minimax Estimators.- Appendix A: Conjugate Points.- Apendix B: Danskinfs Theorem.- References.- List of Corollaries, Definitions, Lemmas, Propositions, Remarks and Theorems
Series: Modern Birkhauser Classics
Originally published as volume 50 in the series: Progress in Mathematics
1st ed. 1984. 2nd printing, 2008, Approx. 245 p. 15 illus., Softcover
ISBN: 978-0-8176-4764-3
About this book
This book is a publication in Swiss Seminars, a subseries of Progress in Mathematics. It is an expanded version of the notes from a seminar on intersection cohomology theory, which met at the University of Bern, Switzerland, in the spring of 1983.
This volume supplies an introduction to the piecewise linear and sheaf-theoretic versions of that theory as developed by M. Goresky and R. MacPherson in Topology 19 (1980), and in Inventiones Mathematicae 72 (1983). While some familiarity with algebraic topology and sheaf theory is assumed, the notes include a self-contained account of further material on constructibility, derived categories, Verdier duality, biduality, and on stratified spaces, which is used in the second paper but not found in standard texts.
Table of contents
Introduction to Piecewise Linear Intersection Homology.-From PL to Sheaf Theory.-A Sample Computation of Intersection Homology.-Pseudomanifold Structures on Complex Analytic Spaces.-Sheaf Theoretic Intersection Cohomology.-Les Foncteurs de la Categorie des Faisceaux Associes a une Application Continue.-Witt Space Cobordism Theory.-Lefschetz Fixed Point Theorem and Intersection Homology.-Problems and Bibliography on Intersection Homology.-References.
Series: Modern Birkhauser Classics
Originally published in the series: Birkhauser Advanced Texts
2nd ed. 2001. 2nd printing, 2008, Approx. 435 p. 48 illus., Softcover
ISBN: 978-0-8176-4766-7
About this textbook
One of the best introductions to differential manifolds available
Includes extensive appendices and detailed diagrams
The basics of differentiable manifolds, global calculus, differential geometry, and related topics constitute a core of information essential for the first or second year graduate student preparing for advanced courses and seminars in differential topology and geometry. Differentiable Manifolds is a text designed to cover this material in a careful and sufficiently detailed manner, presupposing only a good foundation in general topology, calculus, and modern algebra. This second edition contains a significant amount of new material, which, in addition to classroom use, will make it a useful reference text. Topics that can be omitted safely in a first course are clearly marked, making this edition easier to use for such a course, as well as for private study by non-specialists wishing to survey the field.
The themes of linearization, (re) integration, and global versus local calculus are emphasized throughout. Additional features include a treatment of the elements of multivariable calculus, formulated to adapt readily to the global context, an exploration of bundle theory, and a further (optional) development of Lie theory than is customary in textbooks at this level. New to the second edition is a detailed treatment of covering spaces and the fundamental group.
Students, teachers and professionals in mathematics and mathematical physics should find this a most stimulating and useful text.
Table of contents
Preface to the Second Edition.-Topological Manifolds.-The Local Theory of Smooth Functions.-The Global Theory of Smooth Functions.-Flows and Foliations.-Lie Groups and Lie Algebras.-Covectors and 1--Forms.-Multilinear Algebra and Tensors.-Integration of Forms and de Rham Cohomology.-Forms and Foliations.-Riemannian Geometry.-Principal Bundles.-Appendix A. Construction of the Universal Covering.-Appendix B. Inverse Function Theorem.-Appendix C. Ordinary Differential Equations.-Appendix D. The de Rham Cohomology Theorem.-Bibliography.-Index.
Series: Modern Birkhauser Classics
Originally published as a monograph
1st printing 1991. 2nd printing., 2008, Approx. 220 p. 10 illus., Softcover
ISBN: 978-0-8176-4768-1
About this book
Presents a history of an important field in mathematics and philosophy
Focuses on specific topics as to which are not covered elsewhere
Includes articles that are both mathematically technical and easily understood by non-mathematicians
This volume offers insights into the development of mathematical logic over the last century. Arising from a special session of the history of logic at an American Mathematical Society meeting, the chapters explore technical innovations, the philosophical consequences of work during the period, and the historical and social context in which the logicians worked.
The discussions herein will appeal to mathematical logicians and historians of mathematics, as well as philosophers and historians of science.
Table of contents
Acknowledgements.- Contributors.- Jean van Heijenoort(1912-1986).- Introduction.- The Problem of Elimination in the Algebra of Logic.- Peirce and the Law of Distribution.- The First Russell Paradox.- Principia Mathematica and the Development of Automated Theorem Proving.- Oswald Veblen and the origins of Mathematical Logic at Princeton.- The Lowenheim-Skolem Theorem, Theories of Quantifications, and Proof Theory.- The Reception of Godelfs Incompleteness Theorems.- Godelfs and Some Other Examples of problem Transmutation.- The Development of Self-Reference: Lobfs Theorem.- The Unintended Interpretation of Intuitionistic Logic.- The Writing of Introduction to Metamathematics.- In Memoriam: Haskell Brooks Curry.- The Work of J. Richard Buchi.- Index Nominum